Subgroups — C₁₁×C₁₃×#1035 #28384652

Order 14300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×C₁₃×AGL(1,𝔽₅)	—	5	1	no	maximal
4	D₅×C₁₁×C₁₃	—	5	1	no	—
5	C₁₃×#1035	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×#1035	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic
8	C₁₃×D₂₅	C₂×C₁₁	1	1	yes	characteristic
9	C₄×C₁₁×C₁₃	—	25	1	no	Hall
10	C₁₁×D₂₅	C₂×C₁₃	1	1	yes	characteristic
11	C₁₃×C₂₅	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₃	—	25	1	no	—
13	C₁₁×C₂₅	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×AGL(1,𝔽₅)	—	5	1	no	—
15	C₁₁×AGL(1,𝔽₅)	—	5	1	no	—
16	C₁₁×C₁₃	#1035	1	1	yes	characteristic, direct product factor, Hall
17	D₅×C₁₃	—	5	1	no	—
18	D₅×C₁₁	—	5	1	no	—
19	#1035	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₅×C₁₁	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic
22	C₄×C₁₃	—	25	1	no	Hall
23	D₂₅	C₂×C₁₁×C₁₃	1	1	yes	characteristic
24	C₄×C₁₁	—	25	1	no	Hall
25	C₂×C₁₃	—	25	1	no	—
26	C₂₅	C₄×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	25	1	no	—
28	AGL(1,𝔽₅)	—	5	1	no	—
29	C₁₃	C₁₁×#1035	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₁	C₁₃×#1035	1	1	yes	characteristic, direct product factor, Sylow
31	D₅	—	5	1	no	—
32	C₅	C₁₁×C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₄	—	25	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	#1035
commutator, hypocenter	C₂₅	C₄×C₁₁×C₁₃
Frattini	C₅	C₁₁×C₁₃×AGL(1,𝔽₅)
Fitting	C₁₁×C₁₃×C₂₅	C₄
socle	C₅×C₁₁×C₁₃	AGL(1,𝔽₅)
prime radical	C₁₁×C₁₃×D₂₅	C₂
cosocle	D₂₅	C₂×C₁₁×C₁₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₁₁×C₁₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₁×C₁₃×C₂₅	C₄	semidirect
5. C₁₃×#1035	C₁₁	direct (N × H)
6. C₁₁×#1035	C₁₃	direct (N × H)
11. C₁₃×C₂₅	C₄×C₁₁	semidirect
13. C₁₁×C₂₅	C₄×C₁₃	semidirect
16. C₁₁×C₁₃	#1035	direct (N × H)
19. #1035	C₁₁×C₁₃	direct (N × H)
26. C₂₅	C₄×C₁₁×C₁₃	semidirect
29. C₁₃	C₁₁×#1035	direct (N × H)
30. C₁₁	C₁₃×#1035	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×C₁₃×D₂₅	2
C₁₁×C₁₃×AGL(1,𝔽₅)	5
C₁₃×#1035	11
C₁₁×#1035	13

Subgroups — C11×C13×#1035 #28384652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃×#1035 #28384652